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Block #223,001

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/22/2013, 4:00:52 PM Β· Difficulty 9.9390 Β· 6,588,072 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
a64c8a20519ebc35083d049a910ea8d09ee4f785c5d088d5ba888d842d5d1233
View on Chainz β†—

Height

#223,001

Difficulty

9.938984

Transactions

1

Size

199 B

Version

2

Bits

09f06140

Nonce

4,415

Timestamp

10/22/2013, 4:00:52 PM

Confirmations

6,588,072

Mined by

⛏️ P2SHAKgiTbagke9hfkPB2Na9G5N62UMJA8ujWZ

Merkle Root

35cb986140f690e52c379df296a5464ddb92d3c7a1e51cac8ee7732eba490223
Transactions (1)
Coinbase35cb986140f690…e7732eba490223
1 in β†’ 1 out10.1100 XPM109 B
AKgiTbag…MJA8ujWZ
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.295 Γ— 10⁹⁡(96-digit number)
52953598964788023395…92450039617687193601
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
5.295 Γ— 10⁹⁡(96-digit number)
52953598964788023395…92450039617687193601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.059 Γ— 10⁹⁢(97-digit number)
10590719792957604679…84900079235374387201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.118 Γ— 10⁹⁢(97-digit number)
21181439585915209358…69800158470748774401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.236 Γ— 10⁹⁢(97-digit number)
42362879171830418716…39600316941497548801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.472 Γ— 10⁹⁢(97-digit number)
84725758343660837433…79200633882995097601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.694 Γ— 10⁹⁷(98-digit number)
16945151668732167486…58401267765990195201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.389 Γ— 10⁹⁷(98-digit number)
33890303337464334973…16802535531980390401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.778 Γ— 10⁹⁷(98-digit number)
67780606674928669946…33605071063960780801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.355 Γ— 10⁹⁸(99-digit number)
13556121334985733989…67210142127921561601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.711 Γ— 10⁹⁸(99-digit number)
27112242669971467978…34420284255843123201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,732,689 XPMΒ·at block #6,811,072 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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